Changes in the shape of joint bones are a possible cause of arthritic joint ailments. For example, bone anomalies can arise in the region of the hip joint which lead to bone collisions in the region of the joint when the leg is moved and—in particular over a longer period—cause attrition. In order to prepare reconstruction treatments, i.e. treatments which restore a suitable shape of the bone, planning is necessary which can be performed with computer assistance. The reshaping of the femoral head, and sometimes of the rim of the joint cavity, is planned in such a way that unnatural collisions between the femoral bone and the acetabulum (joint cavity) in the joint environment are prevented, wherein a natural shape of the femoral head is to be achieved. The basis of such planning has previously been to determine the contour of joint bones on a two-dimensional basis, for example in a particular sectional plane or imaging plane. In the “Journal of Bone and Joint Surgery”, volume 84-B, No. 4, May 2002, pages 556 to 560, Noetzli et al. describe determining the contour of a femoral neck, for which a measuring and angle system is specified, to which reference shall also be made later in this document.